Free Courses Fluids Structures Electronics 3D Design Optics Photonics Materials Installation Python Optimization Safety & Cybersecurity Embedded Software MBSE Digital Mission Engineering STEM NVH Student Teams Semiconductors Indo Kursus Partner Courses My Courses

[Watch & Learn]

This example is taken from Cornell University’s ANSYS AIM Learning Modules

---

Contents

1. Problem Description
2. Learning Goals
3. Pre-Analysis
4. Geometry Creation
5. Mesh
6. Physics Setup
7. Results Evaluation
8. Verification

Problem Description

This problem is taken from: Prantil, V. C., Papadopoulos, C. and Gessler, P. D., Lying by Approximation: The Truth About Finite Element Analysis, Morgan and Claypool (2013). Consider a stepped shaft under an applied axial load, P. A stress concentration is apparent at the step where the cross-sectional area is discontinuous. The cross section is circular.

So the problem becomes amenable, let’s consider a relatively small fillet placed at the step to reduce the stress concentration to a finite value.

The pressure load on the smaller cross-section is 1000 psi. Calculate the axial stress concentration factor and compare it to the formula provided in Roark’s Formulas for Stress and Strain, Warren C. Young and Richard G. Budynas, 2002.

---

Learning Goals

The purpose of this tutorial is to showcase the simplest stress concentration and demonstrate that it can be resolved in 2 or 3 dimensions. Simple one-dimensional elements (i.e. simple axial bar elements) that capture constant stress within an element are insufficient to capture stress concentrations, even when many elements are used. That is to say, when the necessary physics is not contained in the element formulation, so-called h-convergence or using more elements captures “no more” of the solution than does a coars(er) discretization. This tutorial is meant to highlight where it is relatively straightforward to apply FEA and resolve a solution correctly that belies analytical treatment with uniaxial formulae (such as axial_stress = P/A).

---

Pre-Analysis

It is recommended that you make some back-of-the-envelope estimates of expected results before launching into your computer solution. Here:

for which the following formula for the axial stress concentration factor, K, holds (Roark’s Formulas for Stress and Strain, Warren C. Young and Richard G. Budynas, 2002):

We’ll compare the above axial stress concentration factor to the value obtained from Discovery AIM.

---

Geometry Creation

This problem could be simulated in either 2D or 3D by employing the proper geometric assumptions and boundary conditions. Since Discovery AIM provides a 3D capability, there are several simplifications that must be made to the geometry. When the shape is drawn, we want to create a quarter symmetric model of the geometry so that proper supports can be added to the model that do not over constrain the model. By creating these one dimensional supports, we allow the body to be subjected to the forces of the problem while preventing any rigid body translation and/or rotation of the body in space.

The following video shows how to create the quarter symmetric model of stepped shaft.

---

Mesh

In this video, you will learn how to generate hexahedral mesh for the geometry

---

Physics Setup

This video shows how to specify fixed support, symmetry constraints and pressure load on the model.

---

Results Evaluation

In this video, you will see how to evaluate Equivalent Stress and Displacement Magnitude.

---

Verification

In the pre-analysis, the maximum stress was calculated. To verify that our simulation was accurate, a comparison must be made. In order to view the maximum stress of the simulation, Stress YY was evaluated which can be seen in the previous step.

The table below compares the calculated and simulated values for maximum stress in the stepped shaft. There is a less than 5% difference between the finite element calculation and the simulation result.

Calculated Value	Simulated Value	Percent Difference
1376 psi	1310.6 psi	4.75%